## DESCRIPTION ## Vector Projections ## ENDDESCRIPTION ## Tagged by nhamblet ## DBsubject('Calculus') ## DBchapter('Vectors and the Geometry of Space') ## DBsection('The Dot Product') ## Date('6/3/2002') ## TitleText1('Calculus: Early Transcendentals') ## AuthorText1('Stewart') ## EditionText1('6') ## Section1('12.3') ## Problem1('41') ## TitleText2('Calculus: Early Transcendentals') ## AuthorText2('Rogawski') ## EditionText2('1') ## Section2('12.3') ## Problem2('41') ## KEYWORDS('Dot Product', 'Projection', 'Scalar', 'Vector', 'Orthogonal','vector') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a = non_zero_random(-10, 10); $b = random(-10, 10);$c = random(-10, 10); $d = random(-10, 10);$e = random(-10, 10); $f = random(-10, 10);$square = ($a)**2 + ($b)**2 + ($c)**2;$adbecf = $a*$d + $b*$e + $c*$f; $sclr =$adbecf / sqrt($square);$vctr1 = $adbecf *$a / $square;$vctr2 = $adbecf *$b / $square;$vctr3 = $adbecf *$c / $square;$orth1 = $d -$vctr1; $orth2 =$e - $vctr2;$orth3 = $f -$vctr3; BEGIN_TEXT $PAR Let $${\mathbf a}$$ = ($a, $b,$c) and $${\mathbf b}$$ = ($d,$e, $f) be vectors. Find the scalar, vector, and orthogonal projections of $${\mathbf b}$$ onto $${\mathbf a}$$.$PAR Scalar Projection: \{ ans_rule(30) \} END_TEXT ANS(num_cmp($sclr)); BEGIN_TEXT$PAR Vector Projection: $BR (\{ ans_rule(30) \}, END_TEXT ANS(num_cmp($vctr1)); BEGIN_TEXT \{ ans_rule(30) \}, END_TEXT ANS(num_cmp($vctr2)); BEGIN_TEXT \{ ans_rule(30) \}) END_TEXT ANS(num_cmp($vctr3)); BEGIN_TEXT $PAR Orthogonal Projection:$BR (\{ ans_rule(30) \}, END_TEXT ANS(num_cmp($orth1)); BEGIN_TEXT \{ ans_rule(30) \}, END_TEXT ANS(num_cmp($orth2)); BEGIN_TEXT \{ ans_rule(30) \}) END_TEXT ANS(num_cmp(\$orth3)); ENDDOCUMENT();